Tractable circula densities from Fourier series

• Shogo Kato ^[2] ; Arthur Pewsey ^[1] ; M. C. Jones ^[3]
  1. [1] Universidad de Extremadura

     Universidad de Extremadura

     Badajoz, España

     
  2. [2] Institute of Statistical Mathematics, 10-3 Midori-cho, Tachikawa, 190-8562, Tokyo, Japan
  3. [3] School of Mathematics and Statistics, The Open University, Walton Hall, Milton Keynes, MK7 6AA, UK

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• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 31, Nº. 3, 2022, págs. 595-618
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • This article proposes an approach, based on infinite Fourier series, to constructing tractable densities for the bivariate circular analogues of copulas recently coined ‘circulas’. As examples of the general approach, we consider circula densities generated by various patterns of nonzero Fourier coefficients. The shape and sparsity of such arrangements are found to play a key role in determining the properties of the resultant models. The special cases of the circula densities we consider all have simple closed-form expressions involving no computationally demanding normalizing constants and display wide-ranging distributional shapes. A highly successful model identification tool and methods for parameter estimation and goodness-of-fit testing are provided for the circula densities themselves and the bivariate circular densities obtained from them using a marginal specification construction. The modelling capabilities of such bivariate circular densities are compared with those of five existing models in a numerical experiment, and their application illustrated in an analysis of wind directions.